Real Madrid's Emilio Butragueno (L) shakes hands with Bayern Munich club ambassador Paul Breitner after the draw in Nyon.
Bayern Munich will face Real Madrid for a place in the Champions League final.
Chelsea will play Atletico Madrid in the other semi-final, with the first legs taking place on April 22/23 and the return the following week.
Real's pairing against Bayern brings together two clubs who have won the competition 14 times between them.
Five-time winners Bayern, quarter-final conquerors of Manchester United, are the defending champions. They beat fellow German side Borussia Dortmund at Wembley.
Real have won European club football's top prize nine times - but not since 2002.
Real Madrid boss Carlo Ancelotti is looking forward to his team's clash against the defending champions.
Ancelotti, whose side lost their quarter-final second leg 2-0 to Dortmund on Tuesday but went through 3-2 on aggregate, told a press conference: "Yes, we were poor against Dortmund but it doesn't matter because we made it through.
"If we want to win the Champions League we then have to beat everyone, including Bayern.
"The games will be very difficult...but it's not easy for anyone to play Real Madrid either."
The match will see former Barcelona coach Pep Guardiola return to Spain and Ancelotti added: "He is one of the best coaches in the world. They have a great team."
Chelsea will play the first leg in the Spanish capital as they seek to book a place in this season's final in Lisbon.
On the draw, Blues chief executive Ron Gourlay said: "They're all fantastic sides. The important thing to us was to make sure we were in the semi-final.CHAMPIONS LEAGUE
• Chelsea 2, Paris Saint-Germain 0
• Borussia Dortmund 2, Real Madrid 0
• Atletico Madrid 1, Barcelona 0
• Bayern Munich 3, Manchester United 1
"We need to make sure we are totally prepared for these games. I'm sure Jose will make sure we are but we have some important games before that.
"If someone had said at the start of the season we'd be in the Champions League semi-finals and the Premier League (title) shake-up I'd have taken it. This is what we work for all season.
"We have ambition at the club, it's evolving all the time. We'd like to win back the Premier League and add another Champions League win (to the 2012 success).
"The key is to keep building for the future and we're definitely heading in the right direction.
"We're in a good position and everyone's done fantastically well. We can look forward to the next few weeks."
